document.write( "Question 227966: $\"+x-9sqrt%28x%29%2B20=0+\"$ \n" ); document.write( "

Algebra.Com's Answer #169349 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
To solve equations with square roots in them

Eliminate the square roots. To eliminate a square root:
1. Isolate the term with the square root in it
2. Square both sides of the equation. (NOTE: Because of this step you will need to check your answers. Squaring both sides of an equation can introduce what are called extraneous solutions (solutions which make the squared equation true but do not make the original equation true). Extraneous solution, if they exist, must be found by checking and rejected.)
Repeat the above for any remaining square roots until they are all gone.
At this point you will have an equation without square roots. Solve it.
As explained in the note above, you must check your answers in problems like these. Reject any solutions which to do not fit the original equation.

\n" ); document.write( "Let's try this out on your equation:
\n" ); document.write( " $\"x+-9sqrt%28x%29+%2B20+=+0\"$
\n" ); document.write( "1. Eliminate the square root. Isolate the square root term.
\n" ); document.write( "Add 9sqrt(x) to each side:
\n" ); document.write( " $\"x+%2B+20+=+9sqrt%28x%29\"$
\n" ); document.write( "Square both sides:
\n" ); document.write( " $\"%28x+%2B+20%29%5E2+=+%289sqrt%28x%29%29%5E2\"$
\n" ); document.write( "Remember that exponents do not distribute. So you need to use FOIL or the pattern, $\"%28a%2Bb%29%5E2+=+a%5E2+%2B2ab+%2Bb%5E2\"$ to square the left side:
\n" ); document.write( " $\"%28x%29%5E2+%2B+2%28x%29%2820%29+%2B+%2820%29%5E2+=+81x\"$
\n" ); document.write( " $\"x%5E2+%2B40x+%2B400+=+81x\"$
\n" ); document.write( "The square root is now gone. Now we can solve the equation. Since it is a quadratic equation, we'll start by get one side equal to zero (by subtracting 81x):
\n" ); document.write( " $\"0+=+x%5E2+-41x+%2B+400\"$
\n" ); document.write( "We can solve this by factoring or by using the quadratic formula. This will factor into:
\n" ); document.write( " $\"0+=+%28x+-+25%29%28x+-+16%29\"$
\n" ); document.write( "By the Zero Product Property we know that one of the factors must be zero:
\n" ); document.write( " $\"x+-+25+=+0\"$ or $\"x-16+=+0\"$
\n" ); document.write( "Solving these we get:
\n" ); document.write( " $\"x+=+25\"$ or $\"x+=+16\"$

\n" ); document.write( "Now we (must) check the answers in the original equation:
\n" ); document.write( "Checking 25:
\n" ); document.write( " $\"%2825%29+-+9sqrt%2825%29+%2B+20+=+0\"$
\n" ); document.write( " $\"25+-+9%285%29+%2B+20+=+0\"$
\n" ); document.write( " $\"25+-45+%2B+20+=+0\"$
\n" ); document.write( " $\"0+=+0\"$ Check!
\n" ); document.write( "Checking 16:
\n" ); document.write( " $\"%2816%29+-+9sqrt%2816%29+%2B+20+=+0\"$
\n" ); document.write( " $\"16+-+9%284%29+%2B+20+=+0\"$
\n" ); document.write( " $\"16+-36+%2B+20+=+0\"$
\n" ); document.write( " $\"0+=+0\"$ Check!
\n" ); document.write( "So we have two solutions to the original equation: 25 and 16. \n" ); document.write( "

\n" );